Problem: Solve for $x$ and $y$ using elimination. ${2x-3y = -5}$ ${-2x+4y = 12}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $2x$ and $-2x$ cancel out. ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {2x-3y = -5}\thinspace$ to find $x$ ${2x - 3}{(7)}{= -5}$ $2x-21 = -5$ $2x-21{+21} = -5{+21}$ $2x = 16$ $\dfrac{2x}{{2}} = \dfrac{16}{{2}}$ ${x = 8}$ You can also plug ${y = 7}$ into $\thinspace {-2x+4y = 12}\thinspace$ and get the same answer for $x$ : ${-2x + 4}{(7)}{= 12}$ ${x = 8}$